A number of methods exist for optimizing investments in securities such as stocks, bonds, mutual funds, futures and options, among others. At least one known method for optimizing investments in a fluctuating market is dollar cost averaging (DCA). DCA is a method for periodically purchasing units, or units, of a security in a manner such that the average per-unit cost over a plurality of periodic purchases will be less than the average price of the units over the entire period during which an investor makes the periodic purchases. DCA always results in an average per-unit cost lower than the average price, regardless of whether the long-term trend of the market is increasing or declining, as long as the purchase price fluctuates among the periodic purchases. DCA is an alternative to buying a fixed number of units periodically or buying a number of units at only one time with a lump sum of money and hoping that the price of the security increases between the time the units are purchased and the time they are sold.
DCA involves investing a fixed amount of money at regular intervals over an extended period of time. TABLE 1 illustrates the impact of DCA versus purchasing a fixed number of units over twelve periodic purchases.
TABLE 1DCASecurity PriceFixed Number of UnitsUnitsPerformanceUnitsPurchasedPeriodPriceCostPurchasedCost (A)(N)1101001010010211110101009.0939901010011.114101001010010511110101009.0969901010011.11710100101001.0811110101009.0999901010011.11101010010100101111110101009.09129901010011.11Total Cost$1,200$1,200Total Units120120.8Avg. Per-Unit Cost$10$9.93
As seen in TABLE 1, the fixed-dollar purchasing scheme of DCA results in fewer units being purchased when the per-unit price is high and more units being purchased when the per-unit price is low. In DCA, the number of units purchased each period can be expressed as:                     N        =                  A                      P            -                          P              b                                                          {        1        }            where N is the number of units purchased, A is the dollar amount of the purchase, P is the current unit price at which the purchase is made and Pb is a baseline unit price equal to zero. The equation for N is a simple hyperbolic function asymptotic to the N-axis as P approaches zero and asymptotic to the P-axis as P approaches infinity. DCA will always yield an average per-unit cost lower than the average price of the units over the entire period because DCA yields a weighted average, whereas purchasing a fixed number of units will result simply in the average per-unit cost being equal to the average price, which is an un-weighted average. DCA may be considered a weighted averaging because the number of units purchased with the fixed dollar amount varies inversely with the current per-unit price of the security at the time of purchase. That is, when the per-unit price is high, the fixed dollar amount purchases a smaller number of units than when the per-unit price is low. Thus, whenever the unit price of the security varies over a number of purchase periods, the total number of units purchased using DCA will always be greater than the total number of units purchased by purchasing a fixed number of units each period.
A drawback of DCA is that, while the number of units N purchased varies inversely with the price P, an investor is limited to the purchasing only the number of units given by the simple equation, N=A/P. In addition, DCA lacks a gain control that would allow an investor to optimize the DCA method.
The DCA method may also be used for selling units of a security periodically over an extended period. In this scenario, rather than a fixed dollar amount being used to purchase units of a security, a fixed dollar amount of the security is sold each period. However, DCA is not a desirable method for selling securities since the per-unit yield of the units sold would be less than the average price of the units over the extended period. Obviously, it is more desirable that the per-unit yield be greater than the average price.
In view of the foregoing, it is an object of the present invention to provide a method for automatically determining the number of units of a security to be purchased that yields a lower per-unit cost than DCA. It is also an object of the present invention to provide a method that allows an investor to adjust the number of units purchased based upon personal investment goals and/or market conditions. It is another object of the present invention to provide a method that allows an investor to determine the number of units of a security to be sold in each of a number of periods such that the per-unit yield of the units sold is higher than the average price of the security over the number of periods. It is yet another object of the of the present invention to provide a method that allows an investor to adjust the number of units sold based upon personal investment goals and/or market conditions.